While using these methods to traverse the neighborhood around \(v\) , an AgentNet can also identify all the edges between any two visited nodes; intuitively speaking, this allows for a complete understanding of the neighborhood in question. More specifically, if the transition functions of the agent are implemented with a sufficiently expressive method (e.g. with multi-layer perceptrons), then one can show that it is possible to develop a maximally expressive AgentNet implementation, i.e. where each transition function is injective, similarly to GIN in a standard GNN setting [1]}. Together with Lemma REF , this provides a strong statement: it allows for an AgentNet that can distinguish any pair of different \(r\) -hop neighborhoods around \(v\)  (for any finite \(r\)  and \(\Delta \) , where \(\Delta \)  denotes the maximal degree in the graph).
